An "n-overlap" is a word of the form xxx', where x is a nonempty word of length at least n, and x' is a prefix of x of length n. Thus, for example, abcdabcdab is a 2-overlap. A reversed split occurrence of a pattern p is a word of the form xyz where zx matches the pattern.
For n = 0,1,2,3 words achieving the bound a(n) are as follows:
n = 0: 01
n = 1: 0011
n = 2: 010001100111001
n = 3: 0010100110100011111000111010000011101010001100